ln this paper, a generalized cusp is a properly convex manifold with strictly convex boundary that is diffeomorphic to M × [ 0 , ∞ ) M\times [0,\infty ) where M M is a closed Euclidean manifold. These are classified by Ballas, Cooper, and Leitner [J. Topol. 13 (2020), pp. 1455-1496]. The marked moduli space is homeomorphic to a subspace of the space of conjugacy classes of representations of π 1 M \pi _1M . It has one description as a generalization of a trace-variety, and another description involving weight data that is similar to that used to describe semi-simple Lie groups. It is also a bundle over the space of Euclidean similarity (conformally flat) structures on M M , and the fiber is a closed cone in the space of cubic differentials. For 3 3 -dimensional orientable generalized cusps, the fiber is homeomorphic to a cone on a solid torus.
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